| Summary: | The major function of dynamic networks is to sense information from the environment and process the information to the downstream. Therefore how to measure the information transmission ability of a dynamic network is an important topic to evaluate network performance. However, the dynamic behavior of a dynamic network is complex and, despite knowledge of network components, interactions and noises, it is a challenge to measure the information transmission ability of a dynamic network, especially a nonlinear stochastic dynamic network. Based on nonlinear stochastic dynamic system theory, the information transmission ability can be investigated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. To avoid difficulties associated with solving a complex HJI-constrained optimization problem for information transmission ability, the Takagi-Sugeno (T-S) fuzzy model is introduced to approximate the nonlinear stochastic dynamic network by interpolating several local linear stochastic dynamic networks so that a HJI-constrained optimization problem can be replaced by the linear matrix inequalities (LMIs)-constrained optimization problem. The LMI problem can then be efficiently solved for measuring information transmission ability. We found that a more stable (robust) dynamic network has less information transmission ability, and vice versa. Finally, an example of a biochemical network in cellular communication is given to illustrate the measurement of information transmission ability and to confirm the results by using Monte Carlo simulations.
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